The look-elsewhere effect from a unified Bayesian and frequentist perspective

Journal Article · Fri Oct 02 00:00:00 EDT 2020 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2020/10/009· OSTI ID:1838321

Bayer, Adrian E. ^[1]; Seljak, Uroš ^[2]

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1. Univ. of California, Berkeley, CA (United States)
2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

When searching over a large parameter space for anomalies such as events, peaks, objects, or particles, there is a large probability that spurious signals with seemingly high signi ficance will be found. This is known as the look-elsewhere effect and is prevalent throughout cosmology, (astro)particle physics, and beyond. To avoid making false claims of detection, one must account for this effect when assigning the statistical significance of an anomaly. This is typically accomplished by considering the trials factor, which is generally computed numerically via potentially expensive simulations. In this paper we develop a continuous generalization of the Bonferroni and Sidak corrections by applying the Laplace approximation to evaluate the Bayes factor, and in turn relating the trials factor to the prior-to-posterior volume ratio. Here, we use this to define a test statistic whose frequentist properties have a simple interpretation in terms of the global p-value, or statistical significance. We apply this method to various physics-based examples and show it to work well for the full range of p-values, i.e. in both the asymptotic and non-asymptotic regimes. We also show that this method naturally accounts for other model complexities such as additional degrees of freedom, generalizing Wilks' theorem. This provides a fast way to quantify statistical significance in light of the look-elsewhere effect, without resorting to expensive simulations.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: National Aeronautics and Space Administration (NASA); National Science Foundation (NSF); USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1838321
• Alternate ID(s): OSTI ID: 23041427
• Journal Information: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 10 Vol. 2020; ISSN 1475-7516
• Publisher: Institute of Physics (IOP)
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS